I have done lot of RNA isolations. Probably you are following the right procedure of isolation. Additionally, you should keep things clean. Use sterile plastic wares if possible. Small tubes RNAse-DNAse free, lab coat clean to begin with, set up you bench clean, in an area where there is less flow of people walking around. Laminar hood not needed, tips- RNAse free, dH2O RNAse free, RNAse away, wipe or sprinkle- just a common sense procedure. Probably dH2O is most important- Change gloves more often- 

Several things can go wrong between Trizol suspension and denaturing (?) Electrophoresis. Trizol:sample ratio, plastic/glassware, buffers, loading dye, electrophoresis combs/tank/buffer etc. I ll suggest you to start over again while strictly adhering to whatever protocol (published?)

Dear Ishfaq,

Homogenize the skin tissue properly. Are you using fresh tissue or tissue kept in RNAlater? In case of RNAlater kept tissue, you have to soak RNAlater properly in prior to homogenization. What is the 260/280 and 260/230 ratio? Use fresh nuclease free water or TE buffer. Have you checked the quality just after the isolation of after few freeze-thaw cycle?

I agree with Koner, Collect tissue directly in RNAse Later, than proceed with subsequent steps